| Label |
Class |
Conductor |
Discriminant |
Rank* |
2-Selmer rank |
Torsion |
$\textrm{End}^0(J_{\overline\Q})$ |
$\textrm{End}^0(J)$ |
$\GL_2\textsf{-type}$ |
Sato-Tate |
Nonmaximal primes |
$\Q$-simple |
\(\overline{\Q}\)-simple |
\(\Aut(X)\) |
\(\Aut(X_{\overline{\Q}})\) |
$\Q$-points |
$\Q$-Weierstrass points |
mod-$\ell$ images |
Locally solvable |
Square Ш* |
Analytic Ш* |
Tamagawa |
Regulator |
Real period |
Leading coefficient |
Igusa-Clebsch invariants |
Igusa invariants |
G2-invariants |
Equation |
| 26244.a.52488.1 |
26244.a |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{3} \cdot 3^{8} \) |
$0$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
3.1920.3 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(9.071632\) |
\(2.015918\) |
$[2668,-999,-833661,27648]$ |
$[2001,167208,18650704,2340385860,52488]$ |
$[\frac{132016790288107}{216},\frac{2067394289221}{81},\frac{1037186631482}{729}]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 4x^4 + 20x^3 + 29x^2 + 16x + 3$ |
| 26244.b.52488.1 |
26244.b |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{3} \cdot 3^{8} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
3.5760.5 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.547437\) |
\(5.889904\) |
\(1.074784\) |
$[76,7641,411651,27648]$ |
$[57,-2730,-108572,-3410376,52488]$ |
$[\frac{2476099}{216},-\frac{3120845}{324},-\frac{9798623}{1458}]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + x^3 - 4x^2 + x - 2$ |
| 26244.c.157464.1 |
26244.c |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{3} \cdot 3^{9} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_6$ |
$4$ |
$0$ |
2.60.2, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(14.148765\) |
\(1.572085\) |
$[60,945,2295,82944]$ |
$[45,-270,3780,24300,157464]$ |
$[\frac{9375}{8},-\frac{625}{4},\frac{875}{18}]$ |
$y^2 + (x^3 + 1)y = 2x^3$ |
| 26244.d.314928.1 |
26244.d |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{9} \) |
$1$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_3)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$6$ |
$0$ |
2.20.3, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.985565\) |
\(12.739642\) |
\(1.395083\) |
$[24,189,1107,-162]$ |
$[72,-918,-3024,-265113,-314928]$ |
$[-6144,1088,\frac{448}{9}]$ |
$y^2 + y = x^6 - 2x^3$ |
| 26244.e.472392.1 |
26244.e |
\( 2^{2} \cdot 3^{8} \) |
\( - 2^{3} \cdot 3^{10} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_3)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(12.048083\) |
\(1.338676\) |
$[356,3969,419553,248832]$ |
$[267,1482,-2884,-741588,472392]$ |
$[\frac{5584059449}{1944},\frac{174127343}{2916},-\frac{5711041}{13122}]$ |
$y^2 + (x^3 + 1)y = 2$ |
